In data storage systems it is known to employ so-called “mapped” logical storage units or MLUs. An MLU is presented to a host computer as a conventional logical storage unit or LUN, i.e., as consisting of a linear array of blocks of storage and having a device (LUN) identifier that enables a host computer to issue I/O requests to write and read data to/from the MLU. Within the data storage system, however, the MLU is mapped to underlying storage in a more arbitrary way in order to provide certain functional and/or performance advantages. In one example an MLU is a so-called “thin” LUN or TLU for which the underlying storage is allocated only on an as-needed basis. Use of TLUs can provide for more efficient use of physical storage resources. At any given time, one or more logical areas or ranges of the MLU have no underlying storage associated therewith, while other logical areas or ranges do. When a host I/O request directed to an MLU is received at a data storage system, it is necessary to map a range of blocks of the request to one or more distinct units of underlying storage, and then to perform the requested operation on the mapped units of underlying storage.